- Email: [email protected]
Development of new device for measuring thermal stresses
Cement and Concrete Research 32 (2002) 1645 – 1651
Development of new device for measuring thermal stresses Jang-Ho Jay Kima, Sang-Eun Jeonb, Jin-Keun Kimb,* a
Department of Civil and Environmental Engineering and Construction Technology Laboratory, Sejong University, 98 Kunja-dong, Kwangjin-gu, Seoul 143-747, South Korea b Department of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, 373-1 Kuseong-dong, Yuseong-gu, Taejon 305-701, South Korea Received 18 July 2001; accepted 30 April 2002
Abstract In recent years, numerous analytical and experimental researches have been performed on the prediction of thermal stresses in mass concrete structures. However, due to the difficulty of the problem, limitations still exist for both analytical and experimental methods of measuring thermal stresses in mass concrete. In this research, a new experimental device measuring thermal stresses directly in a laboratory setting is developed. The equipment is located in a temperature chamber that follows the temperature history, which has been previously obtained from temperature distribution analyses. Thermal forces are measured continuously by two load cells in the device. The results show that the thermal stresses estimated by the newly developed device agree well with general stress variations in actual structures. D 2002 Published by Elsevier Science Ltd. Keywords: Thermal stress; Modulus of elasticity; Coefficient of thermal expansion; Developed device; Degree of constraint
1. Introduction When constructing structures using mass concrete or high-strength concrete, specific thermal stress produced in a structure due to the hydration heat of cement could pose a serious problem to the integrity of structures. Specific thermal stress damages a structure and degrades the structural serviceability, water tightness, and durability. Therefore, estimating the existing thermal stresses and the thermal cracks in concrete structures becomes vital. Specific thermal stresses are calculated by finite element method (FEM), which is the most commonly used analytical method, and are measured by experimental methods using a special equipment or gauge in actual and simulated structures or a thermal stress measuring device in controlled laboratory setting equipment. With respect to the analytical methods, a fundamental limitation is derived from the difficulty of predicting concrete properties, such as modulus of elasticity, coefficient of thermal expansion, and others. The problems with experimentally obtained results are their economic inefficiency and uncertainty related to field conditions. * Corresponding author. Tel.: +82-42-869-3614; fax: +82-42-869-3610. E-mail address: [email protected] (J.-K. Kim). 0008-8846/02/$ – see front matter D 2002 Published by Elsevier Science Ltd. PII: S 0 0 0 8 - 8 8 4 6 ( 0 2 ) 0 0 8 4 2 - 6
Therefore, developing a laboratory or controlled experimental device that can accurately measure thermal stresses of concrete with various mixing proportion and multiple loading conditions is urgently needed. In Japan and Europe, experimental laboratory equipment were invented and researches have been actively pursued since early 1980s. Tazawa and Iida [1] investigated hydration heat-induced thermal stresses in concrete and their mechanism using thermal crack experimental apparatus. Aokage et al. [2] also experimentally measured effective modulus of elasticity of mass concrete with a similar apparatus. In Germany, the Technical University of Munich (TUM) developed an experimental tool called ‘‘cracking frame’’ and estimated thermal stresses and cracking pattern of early age concrete [3– 5]. TUM also invented the Temperature Stress Testing Machine (TSTM), a modified version of the cracking frame [6,7]. In this study, a laboratory test device measuring thermal stress was developed. The developed device can easily control the experimental variables, such as coefficient of thermal expansion of concrete and other cement-based materials. It is also designed to quantitatively measure the change of thermal stresses in various environmental conditions using a temperature and humidity chamber.
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2. Development of thermal stress measuring device 2.1. Background Fig. 1 shows the basic concepts in developing a thermal stress measuring device. It is important to note that the thermal expansion coefficient of the frame material is different from that of concrete. When concrete and frame material are applied with same strains under the prescribed temperature history (Fig. 1(a)), the variation of resultant stresses is dependent on thermal expansion coefficient of the frame material. More specifically, when a frame material with lower thermal expansion coefficient than that of concrete is used, this setup produces thermal stresses at interior of structures subjected to internal restraint or whole section of structures subjected to external restraint in actual structures (Fig. 1(b)). However, if a frame material with higher thermal expansion is used, this setup produces thermal stresses at the surface of structures subjected to internal restraint in actual structures (Fig. 1(c)). Based on the above concept and ‘‘cracking frame’’ design, the thermal stress measuring device is developed. This system can effectively measure thermal stresses within concrete specimens in a laboratory, offsetting uncertain properties of concrete. Fig. 2 shows the overall design of the system and the detailed descriptions of the device. The shape and dimensions of the device is similar to that of the ‘‘cracking frame’’ invented in Germany. The experimental procedures follow the procedures used for the thermal crack apparatus developed in Japan. However, the developed device is less expensive to manufacture and enhances the weaknesses that existed in the previously developed apparatuses. Temperature control of ‘‘cracking frame’’ was based on a semiadiabatic condition using wood and polystyrene, and thermal crack apparatus used thin
copper or polyethylene plate to prevent drying shrinkage. However, the developed device is tested in a temperature and humidity chamber where the applied temperature is defined by a user and the humidity of over 85% is maintained to minimize drying. 2.2. Experimental method Two load cells are used for measuring restrained forces in a frame. Thermocouples or temperature gauge are set at a chamber, frame, and concrete specimens to ascertain the applied temperature. To reduce plastic and drying shrinkages from occurring in concrete specimens at early ages, humidity is kept at over 85%. Effect of hydration heat on the applied temperature is ignored since the depth of specimens is no more than 80 mm (Fig. 2) and thermal transfer is active at open surfaces of a concrete specimen. The left and right side surfaces of the specimen indicated as a dotted line in Fig. 2 is covered with thin steel plates before placing concrete. The plates are removed 6 h later. Also, friction between specimen and thin bottom plate supporting a frame is minimized by painting grease and oil on the thin steel plate. The application of lubrication during the test is controlled based on preliminary examinations. To predict thermal stresses in structures using the developed device, a temperature analysis is first performed, followed by experiments at a temperature and humidity chamber preprogrammed based on analysis results. To eliminate the unknown and external factors of experiments, the developed frame and specimen materials such as aggregates and water are kept at a constant temperature by storing them in the same temperature and humidity chamber before casting of specimens. Even though painstaking effort has been undertaken to control the temperature of the specimens and the frame, temper-
Fig. 1. Concepts of the development of thermal stress measuring device. (a) Prescribed temperature history. (b) Frame material with lower thermal expansion coefficient than that of concrete. (c) Frame material with higher thermal expansion than that of concrete.
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Fig. 2. Shape and dimensions of the developed device.
ature changes can occur due to the transportation and other procedures before and during the experiment. Therefore, the chamber is fixed at a required initial temperature for 6 h after placing the frame and concrete specimen before the test. Then, the chamber is programmed to follow the required temperature history. 2.3. Measurement of thermal stresses For the prediction of thermal stresses, uncertainties in material properties of early age concrete such as elastic modulus and coefficient of thermal expansion can be ignored using the developed device. More specifically, concrete specimens are placed in a frame attached with various metal plates of different thermal expansion coefficient. This frame setup under a known temperature history allows prediction of thermal stresses in concrete structures with a fully restrained condition. Under a fully restrained condition, thermal stress of concrete is expressed as (Eq. (1)) fc;res ¼
Fc;res Ac
ð1Þ
where, fc,res and Fc,res are thermal stress and force of concrete at fully restrained condition, respectively; and Ac is the cross-sectional area of the concrete specimen in the frame. However, an application of the fully restrained condition is not feasible in this device. Therefore, the evaluated stress is modified and expressed as (Eq. (2)) fc ¼
Fc Ac
ð2Þ
where fc and Fc are the evaluated stress and force from a concrete specimen, respectively.
In the same manner, the evaluated stress of the frame is expressed as fs ¼
Fs As
ð3Þ
where fs and Fs are the evaluated stress and force of the frame, respectively, and As is the cross-sectional area of the frame. A force equilibrium condition of the frame and the concrete specimen can be expressed as fs A s ¼ A c fc :
ð4Þ
Inserting Eq. (3) into Eq. (4) and solving for fc, the thermal stress of concrete is expressed as fc ¼
F 0 Fcomp Fs ¼ s Ac Ac
ð5Þ
where Fs0 is the measured force from load cells and Fcomp refers to the compensation forces of load cells. Compensation force is induced by temperature compensation of load cells, which can be obtained from preliminary tests. Under the same temperature and humidity conditions to that of the main test, the preliminary tests were performed prior to casting concrete to estimate the temperature compensation force of the developed system with load cells. Once the values for Fs and Ac at a specific time are experimentally obtained, thermal stress of an early age concrete can be calculated using Eq. (5). It is important to note that the thermal stress of early age concrete can be calculated even though its elastic modulus and thermal expansion coefficient are uncertain.
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Table 1 Materials used in the experiments and their properties Material
Thermal expansion coefficient ( 10 6/C)
Modulus of elasticity ( 104 MPa)
Concrete Steel Aluminum Invar
10 11 24 4.5
2.94 20.6 7.18 2.83
2.4. Degree of constraint in the device To reproduce variable restrained conditions like that of the TSTM, metal plates with a different coefficient of thermal expansion from that of concrete are set between two crossheads of the device. Fig. 2 shows the core of the developed device with metal plates between two crossheads. Theoretically, if the coefficient of thermal expansion or conductivity of the metal plates is zero, then fully or 100% restrained condition can be reproduced. However, a material with zero coefficient of thermal expansion does not exist. Therefore, materials with various coefficients of thermal expansion are used to effectively reproduce internal and external restrained conditions as described previously. Metal plates with various cross-sectional areas as well as coefficient of thermal expansions can vary the degree of constraint. This variation of the degree of constraint can be obtained from the following mathematical procedures. In this developed device, the constraint force of concrete specimen is actually obtained from constraint metals and load cells. From the same axial displacement condition (dl + dm = dc), the following equation is obtained. Fs Fs ll al DT þ þ lm am DT þ El Al Em Am Fs ¼ lc ac DT ð6Þ Ec Ac where, l, a, and E are length, coefficient of thermal expansion, and elastic modulus, correspondingly. Subscripts l, m, and c represent load cell, constraint metal, and concrete, correspondingly. From Eq. (6), the constraint force Fs is expressed as Fs ¼
lc ac ll al lm am DT : ll =ðEl Al Þ þ lm =ðEm Am Þ þ lc =ðEc Ac Þ
ð7Þ
Since lc = lm + ll, Eq. (7) can be modified as Fs ¼
ðac al Þll þ ðac am Þlm DT : 1 1 1 1 þ þ ll þ lm El Al Ec Ac Em Am Ec Ac
ð8Þ
If Ec and Ac are constants in Eq. (8), the constraint force increases with the difference of coefficient of thermal expansion between concrete and frame materials (i.e., load cells and constraint metals) denoted as (ac al) or (ac am), and axial stiffness of frame denoted as (ElAl)/ll or (EmAm)/lm.
Therefore, the degree of constraint in the developed device can be varied by using frames with various coefficients of thermal expansion and cross-sectional areas. Additionally, by directly measuring the displacement of a concrete specimen in the developed device, dc, with linear displacement transducers, uncertain material properties of early age concrete such as modulus of elasticity and coefficient of thermal expansion can be evaluated from Eq. (6). Table 1 tabulates various materials used for a verification of the developed device and their thermal expansion coefficients and elastic moduli.
3. Experimental results 3.1. Concrete test results 3.1.1. Mix proportion The detailed mix proportion of concrete is shown in Table 2. 3.1.2. Mechanical characteristic of concrete In this study, experiments for two representative cases are performed. One is the interior of concrete structures subjected to internal restraint or the whole section subjected to external restraints. The other is the surface of concrete structures subject to internal restraint. For these cases, concrete cylinder specimens with f 100 200 mm are cured at different temperature histories shown in Fig. 3(a) and Fig. 4(a). Table 3 shows test results for compressive and tensile strengths and elastic moduli of concrete. The experiment is performed for 4 days in a temperature and humidity chamber. Cylinder specimens are cured under the same temperature and humidity conditions as those from the experiments with the developed device. As shown in Table 3, the concrete compressive and tensile strengths and elastic moduli for interior location are relatively higher than those located at the surface. This is due to the difference in the concrete maturity even when the specimen is cast from the same batch. 3.2. Test results in the developed system 3.2.1. Plate material (aluminum) with higher thermal expansion coefficient than concrete To verify the validity of the developed device, tests using aluminum plate, which has a higher coefficient of Table 2 Mix proportion of concrete Unit content (kg/m3) W/C
S/A
Water
Cement
Fine aggregate
Coarse aggregate
Admixture
0.5
0.42
181
360
707
989
1.81
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to note that the measured temperatures of the concrete specimen, the frame, and the temperature chamber are similar to the temperatures calculated from the analysis
Fig. 3. Test results in aluminum frame (W/C = 0.5, tension is positive). (a) Temperature history. (b) Restrained load of frame. (c) Stress of concrete.
thermal expansion than that of concrete, is performed. Fig. 3(a) shows the measured temperatures of the concrete, aluminum plate, and chamber. In Fig. 3(a), it is important
Fig. 4. Test results in invar frame (W/C = 0.5, tension is positive). (a) Temperature history. (b) Restrained load of frame. (c) Stress of concrete.
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(within 1% of error). Therefore, the assumption of ignoring hydration heat of cement in concrete specimen is validated. Fig. 3(b) shows the variation of restrained load of the frame with time. In Fig. 3(b), it is important to note that the compressive loads are measured in the initial stage followed by the measurement of tensile loads during the descending part of the temperature curve. Using the restrained loads in Fig. 3(b), restrained thermal stresses acting on the concrete specimen are computed by Eq. (4) as shown in Fig. 3(c). Fig. 3(c) is similar to the variation of thermal stresses appearing in the surface of mass concrete structures [8]. Generally, thermal stresses initially are tensile and decrease gradually after the peak values at surfaces of structures. This is due to the fact that differential volume change based on temperature distribution is restrained by continuity of cross-section, which is called ‘‘internal restraint.’’ Therefore, it is safe to assume that the developed system can reproduce thermal stresses at surfaces of a structure subjected to internal restrained condition. 3.2.2. Plate material (invar) with lower thermal expansion coefficient than concrete Fig. 4 shows the results from the experiment using invar plates. Fig. 4(a) shows a similar tendency as the test results obtained using aluminum plate. Fig. 4(c), however, indicates that the developed device can reproduce thermal stresses at the interior of structures subjected to internal restraint or the whole section of structures subjected to external restraint. To verify Eq. (8), an equation representing numerical constraint forces, the computed stresses using Eq. (8) are compared to the experimentally obtained stresses of concrete using aluminum plates (Fig. 5). In this calculation, temperature history in Fig. 3(a) and measured elastic modulus of concrete in Section 3.1.2 were used. Furthermore, the following data are used in the calculation: coefficient of thermal expansion of 12.0 10 6/C for concrete and load cell and 24.0 10 6/C for aluminum plates, length of 9.6 and 24.0 cm for load cell and aluminum plates, respectively, and elastic moduli of 20.6 and 7.18 MPa for load cell and aluminum plates, respectively. In Fig. 5, the difference between calculated and experimental results is due to
Fig. 5. Comparison between experimental and calculated results.
the inaccurate input data, such as properties of load cell and concrete as well as inelastic deformation due to creep of concrete.
4. Conclusions From the results obtained using the developed thermal stress measuring device, the following conclusions can be drawn. 1. This device shows the possibility of measuring thermal stress variations of any position in concrete structures using different thermal expansion coefficient plates even though properties of concrete are uncertain. 2. The application of various degrees of constraint can be achieved by using constraint frame material with different thermal expansion coefficient and crosssectional area than those of concrete. 3. A commercialized chamber, which is able to control temperature and humidity, can be used with this developed device.
Acknowledgments
Table 3 Mechanical properties of concrete
Age (days)
Compressive strength (MPa)
Splitting tensile strength (MPa)
Modulus of elasticity ( 104 MPa)
Surface
Interior
Surface
Interior
Surface
Interior
1 2 3
18.4 23.4 26.0
25.4 33.9 34.3
2.59 2.95 3.25
3.04 3.60 3.69
1.96 2.25 2.55
2.65 2.74 2.94
This research was supported by the National Research Laboratory program of Year 2000 (2000-NNL-01-C-033) from the Ministry of Science and Technology of Korea for the development of cracking Control Technique of Concrete Structure. This support is deeply appreciated. The financial support to the first author by a fund of the National Research Laboratory program of Year 2000 (2000-N-NL-01-C-162) is also gratefully appreciated.
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References [1] E. Tazawa, K. Iida, Mechanism of thermal stress generation due to hydration heat of concrete, Trans. Jpn. Concr. Inst. 5 (1983) 119 – 126. [2] H. Aokage, Y. Ito, N. Watanabe, Experimental study on effective modulus of elasticity in massive concrete, Trans. Jpn. Concr. Inst. 8 (1986) 119 – 124. [3] RILEM TC 119-TCE, Avoidance of Thermal Cracking in Concrete at Early Ages, 1997. [4] R. Breitenbucher, Investigation of thermal cracking with the crackingframe, Mater. Struct. 23 (1990) 172 – 177. [5] R. Springenschmid, R. Breitenbucher, M. Mangold, Development of the cracking frame and the temperature-stress testing machine, Proceed-
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ings of the International RILEM Symposium: Thermal Cracking in Concrete at Early Ages, E&FN Spon, 1994, pp. 137 – 144. [6] G. Thielen, W. Hintzen, Investigation of concrete behaviour under restraint with a temperature-stress test machine, Proceedings of the International RILEM Symposium: Thermal Cracking in Concrete at Early Ages, E&FN Spon, 1994, pp. 145 – 152. [7] K. Schoppel, M. Plannerer, R. Springenschmid, Determination of restraint stresses and of material properties during hydration of concrete with the temperature – stress testing machine, Proceedings of the International RILEM Symposium: Thermal Cracking in Concrete at Early Ages, E&FN Spon, 1994, pp. 153 – 160. [8] Korea Electric Power Research Institute, Reduction of Hydration Heat in Concrete Structures, 1998 (in Korean).
Development of new device for measuring thermal stresses Jang-Ho Jay Kima, Sang-Eun Jeonb, Jin-Keun Kimb,* a
Department of Civil and Environmental Engineering and Construction Technology Laboratory, Sejong University, 98 Kunja-dong, Kwangjin-gu, Seoul 143-747, South Korea b Department of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, 373-1 Kuseong-dong, Yuseong-gu, Taejon 305-701, South Korea Received 18 July 2001; accepted 30 April 2002
Abstract In recent years, numerous analytical and experimental researches have been performed on the prediction of thermal stresses in mass concrete structures. However, due to the difficulty of the problem, limitations still exist for both analytical and experimental methods of measuring thermal stresses in mass concrete. In this research, a new experimental device measuring thermal stresses directly in a laboratory setting is developed. The equipment is located in a temperature chamber that follows the temperature history, which has been previously obtained from temperature distribution analyses. Thermal forces are measured continuously by two load cells in the device. The results show that the thermal stresses estimated by the newly developed device agree well with general stress variations in actual structures. D 2002 Published by Elsevier Science Ltd. Keywords: Thermal stress; Modulus of elasticity; Coefficient of thermal expansion; Developed device; Degree of constraint
1. Introduction When constructing structures using mass concrete or high-strength concrete, specific thermal stress produced in a structure due to the hydration heat of cement could pose a serious problem to the integrity of structures. Specific thermal stress damages a structure and degrades the structural serviceability, water tightness, and durability. Therefore, estimating the existing thermal stresses and the thermal cracks in concrete structures becomes vital. Specific thermal stresses are calculated by finite element method (FEM), which is the most commonly used analytical method, and are measured by experimental methods using a special equipment or gauge in actual and simulated structures or a thermal stress measuring device in controlled laboratory setting equipment. With respect to the analytical methods, a fundamental limitation is derived from the difficulty of predicting concrete properties, such as modulus of elasticity, coefficient of thermal expansion, and others. The problems with experimentally obtained results are their economic inefficiency and uncertainty related to field conditions. * Corresponding author. Tel.: +82-42-869-3614; fax: +82-42-869-3610. E-mail address: [email protected] (J.-K. Kim). 0008-8846/02/$ – see front matter D 2002 Published by Elsevier Science Ltd. PII: S 0 0 0 8 - 8 8 4 6 ( 0 2 ) 0 0 8 4 2 - 6
Therefore, developing a laboratory or controlled experimental device that can accurately measure thermal stresses of concrete with various mixing proportion and multiple loading conditions is urgently needed. In Japan and Europe, experimental laboratory equipment were invented and researches have been actively pursued since early 1980s. Tazawa and Iida [1] investigated hydration heat-induced thermal stresses in concrete and their mechanism using thermal crack experimental apparatus. Aokage et al. [2] also experimentally measured effective modulus of elasticity of mass concrete with a similar apparatus. In Germany, the Technical University of Munich (TUM) developed an experimental tool called ‘‘cracking frame’’ and estimated thermal stresses and cracking pattern of early age concrete [3– 5]. TUM also invented the Temperature Stress Testing Machine (TSTM), a modified version of the cracking frame [6,7]. In this study, a laboratory test device measuring thermal stress was developed. The developed device can easily control the experimental variables, such as coefficient of thermal expansion of concrete and other cement-based materials. It is also designed to quantitatively measure the change of thermal stresses in various environmental conditions using a temperature and humidity chamber.
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2. Development of thermal stress measuring device 2.1. Background Fig. 1 shows the basic concepts in developing a thermal stress measuring device. It is important to note that the thermal expansion coefficient of the frame material is different from that of concrete. When concrete and frame material are applied with same strains under the prescribed temperature history (Fig. 1(a)), the variation of resultant stresses is dependent on thermal expansion coefficient of the frame material. More specifically, when a frame material with lower thermal expansion coefficient than that of concrete is used, this setup produces thermal stresses at interior of structures subjected to internal restraint or whole section of structures subjected to external restraint in actual structures (Fig. 1(b)). However, if a frame material with higher thermal expansion is used, this setup produces thermal stresses at the surface of structures subjected to internal restraint in actual structures (Fig. 1(c)). Based on the above concept and ‘‘cracking frame’’ design, the thermal stress measuring device is developed. This system can effectively measure thermal stresses within concrete specimens in a laboratory, offsetting uncertain properties of concrete. Fig. 2 shows the overall design of the system and the detailed descriptions of the device. The shape and dimensions of the device is similar to that of the ‘‘cracking frame’’ invented in Germany. The experimental procedures follow the procedures used for the thermal crack apparatus developed in Japan. However, the developed device is less expensive to manufacture and enhances the weaknesses that existed in the previously developed apparatuses. Temperature control of ‘‘cracking frame’’ was based on a semiadiabatic condition using wood and polystyrene, and thermal crack apparatus used thin
copper or polyethylene plate to prevent drying shrinkage. However, the developed device is tested in a temperature and humidity chamber where the applied temperature is defined by a user and the humidity of over 85% is maintained to minimize drying. 2.2. Experimental method Two load cells are used for measuring restrained forces in a frame. Thermocouples or temperature gauge are set at a chamber, frame, and concrete specimens to ascertain the applied temperature. To reduce plastic and drying shrinkages from occurring in concrete specimens at early ages, humidity is kept at over 85%. Effect of hydration heat on the applied temperature is ignored since the depth of specimens is no more than 80 mm (Fig. 2) and thermal transfer is active at open surfaces of a concrete specimen. The left and right side surfaces of the specimen indicated as a dotted line in Fig. 2 is covered with thin steel plates before placing concrete. The plates are removed 6 h later. Also, friction between specimen and thin bottom plate supporting a frame is minimized by painting grease and oil on the thin steel plate. The application of lubrication during the test is controlled based on preliminary examinations. To predict thermal stresses in structures using the developed device, a temperature analysis is first performed, followed by experiments at a temperature and humidity chamber preprogrammed based on analysis results. To eliminate the unknown and external factors of experiments, the developed frame and specimen materials such as aggregates and water are kept at a constant temperature by storing them in the same temperature and humidity chamber before casting of specimens. Even though painstaking effort has been undertaken to control the temperature of the specimens and the frame, temper-
Fig. 1. Concepts of the development of thermal stress measuring device. (a) Prescribed temperature history. (b) Frame material with lower thermal expansion coefficient than that of concrete. (c) Frame material with higher thermal expansion than that of concrete.
J.-H.J. Kim et al. / Cement and Concrete Research 32 (2002) 1645–1651
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Fig. 2. Shape and dimensions of the developed device.
ature changes can occur due to the transportation and other procedures before and during the experiment. Therefore, the chamber is fixed at a required initial temperature for 6 h after placing the frame and concrete specimen before the test. Then, the chamber is programmed to follow the required temperature history. 2.3. Measurement of thermal stresses For the prediction of thermal stresses, uncertainties in material properties of early age concrete such as elastic modulus and coefficient of thermal expansion can be ignored using the developed device. More specifically, concrete specimens are placed in a frame attached with various metal plates of different thermal expansion coefficient. This frame setup under a known temperature history allows prediction of thermal stresses in concrete structures with a fully restrained condition. Under a fully restrained condition, thermal stress of concrete is expressed as (Eq. (1)) fc;res ¼
Fc;res Ac
ð1Þ
where, fc,res and Fc,res are thermal stress and force of concrete at fully restrained condition, respectively; and Ac is the cross-sectional area of the concrete specimen in the frame. However, an application of the fully restrained condition is not feasible in this device. Therefore, the evaluated stress is modified and expressed as (Eq. (2)) fc ¼
Fc Ac
ð2Þ
where fc and Fc are the evaluated stress and force from a concrete specimen, respectively.
In the same manner, the evaluated stress of the frame is expressed as fs ¼
Fs As
ð3Þ
where fs and Fs are the evaluated stress and force of the frame, respectively, and As is the cross-sectional area of the frame. A force equilibrium condition of the frame and the concrete specimen can be expressed as fs A s ¼ A c fc :
ð4Þ
Inserting Eq. (3) into Eq. (4) and solving for fc, the thermal stress of concrete is expressed as fc ¼
F 0 Fcomp Fs ¼ s Ac Ac
ð5Þ
where Fs0 is the measured force from load cells and Fcomp refers to the compensation forces of load cells. Compensation force is induced by temperature compensation of load cells, which can be obtained from preliminary tests. Under the same temperature and humidity conditions to that of the main test, the preliminary tests were performed prior to casting concrete to estimate the temperature compensation force of the developed system with load cells. Once the values for Fs and Ac at a specific time are experimentally obtained, thermal stress of an early age concrete can be calculated using Eq. (5). It is important to note that the thermal stress of early age concrete can be calculated even though its elastic modulus and thermal expansion coefficient are uncertain.
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Table 1 Materials used in the experiments and their properties Material
Thermal expansion coefficient ( 10 6/C)
Modulus of elasticity ( 104 MPa)
Concrete Steel Aluminum Invar
10 11 24 4.5
2.94 20.6 7.18 2.83
2.4. Degree of constraint in the device To reproduce variable restrained conditions like that of the TSTM, metal plates with a different coefficient of thermal expansion from that of concrete are set between two crossheads of the device. Fig. 2 shows the core of the developed device with metal plates between two crossheads. Theoretically, if the coefficient of thermal expansion or conductivity of the metal plates is zero, then fully or 100% restrained condition can be reproduced. However, a material with zero coefficient of thermal expansion does not exist. Therefore, materials with various coefficients of thermal expansion are used to effectively reproduce internal and external restrained conditions as described previously. Metal plates with various cross-sectional areas as well as coefficient of thermal expansions can vary the degree of constraint. This variation of the degree of constraint can be obtained from the following mathematical procedures. In this developed device, the constraint force of concrete specimen is actually obtained from constraint metals and load cells. From the same axial displacement condition (dl + dm = dc), the following equation is obtained. Fs Fs ll al DT þ þ lm am DT þ El Al Em Am Fs ¼ lc ac DT ð6Þ Ec Ac where, l, a, and E are length, coefficient of thermal expansion, and elastic modulus, correspondingly. Subscripts l, m, and c represent load cell, constraint metal, and concrete, correspondingly. From Eq. (6), the constraint force Fs is expressed as Fs ¼
lc ac ll al lm am DT : ll =ðEl Al Þ þ lm =ðEm Am Þ þ lc =ðEc Ac Þ
ð7Þ
Since lc = lm + ll, Eq. (7) can be modified as Fs ¼
ðac al Þll þ ðac am Þlm DT : 1 1 1 1 þ þ ll þ lm El Al Ec Ac Em Am Ec Ac
ð8Þ
If Ec and Ac are constants in Eq. (8), the constraint force increases with the difference of coefficient of thermal expansion between concrete and frame materials (i.e., load cells and constraint metals) denoted as (ac al) or (ac am), and axial stiffness of frame denoted as (ElAl)/ll or (EmAm)/lm.
Therefore, the degree of constraint in the developed device can be varied by using frames with various coefficients of thermal expansion and cross-sectional areas. Additionally, by directly measuring the displacement of a concrete specimen in the developed device, dc, with linear displacement transducers, uncertain material properties of early age concrete such as modulus of elasticity and coefficient of thermal expansion can be evaluated from Eq. (6). Table 1 tabulates various materials used for a verification of the developed device and their thermal expansion coefficients and elastic moduli.
3. Experimental results 3.1. Concrete test results 3.1.1. Mix proportion The detailed mix proportion of concrete is shown in Table 2. 3.1.2. Mechanical characteristic of concrete In this study, experiments for two representative cases are performed. One is the interior of concrete structures subjected to internal restraint or the whole section subjected to external restraints. The other is the surface of concrete structures subject to internal restraint. For these cases, concrete cylinder specimens with f 100 200 mm are cured at different temperature histories shown in Fig. 3(a) and Fig. 4(a). Table 3 shows test results for compressive and tensile strengths and elastic moduli of concrete. The experiment is performed for 4 days in a temperature and humidity chamber. Cylinder specimens are cured under the same temperature and humidity conditions as those from the experiments with the developed device. As shown in Table 3, the concrete compressive and tensile strengths and elastic moduli for interior location are relatively higher than those located at the surface. This is due to the difference in the concrete maturity even when the specimen is cast from the same batch. 3.2. Test results in the developed system 3.2.1. Plate material (aluminum) with higher thermal expansion coefficient than concrete To verify the validity of the developed device, tests using aluminum plate, which has a higher coefficient of Table 2 Mix proportion of concrete Unit content (kg/m3) W/C
S/A
Water
Cement
Fine aggregate
Coarse aggregate
Admixture
0.5
0.42
181
360
707
989
1.81
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to note that the measured temperatures of the concrete specimen, the frame, and the temperature chamber are similar to the temperatures calculated from the analysis
Fig. 3. Test results in aluminum frame (W/C = 0.5, tension is positive). (a) Temperature history. (b) Restrained load of frame. (c) Stress of concrete.
thermal expansion than that of concrete, is performed. Fig. 3(a) shows the measured temperatures of the concrete, aluminum plate, and chamber. In Fig. 3(a), it is important
Fig. 4. Test results in invar frame (W/C = 0.5, tension is positive). (a) Temperature history. (b) Restrained load of frame. (c) Stress of concrete.
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(within 1% of error). Therefore, the assumption of ignoring hydration heat of cement in concrete specimen is validated. Fig. 3(b) shows the variation of restrained load of the frame with time. In Fig. 3(b), it is important to note that the compressive loads are measured in the initial stage followed by the measurement of tensile loads during the descending part of the temperature curve. Using the restrained loads in Fig. 3(b), restrained thermal stresses acting on the concrete specimen are computed by Eq. (4) as shown in Fig. 3(c). Fig. 3(c) is similar to the variation of thermal stresses appearing in the surface of mass concrete structures [8]. Generally, thermal stresses initially are tensile and decrease gradually after the peak values at surfaces of structures. This is due to the fact that differential volume change based on temperature distribution is restrained by continuity of cross-section, which is called ‘‘internal restraint.’’ Therefore, it is safe to assume that the developed system can reproduce thermal stresses at surfaces of a structure subjected to internal restrained condition. 3.2.2. Plate material (invar) with lower thermal expansion coefficient than concrete Fig. 4 shows the results from the experiment using invar plates. Fig. 4(a) shows a similar tendency as the test results obtained using aluminum plate. Fig. 4(c), however, indicates that the developed device can reproduce thermal stresses at the interior of structures subjected to internal restraint or the whole section of structures subjected to external restraint. To verify Eq. (8), an equation representing numerical constraint forces, the computed stresses using Eq. (8) are compared to the experimentally obtained stresses of concrete using aluminum plates (Fig. 5). In this calculation, temperature history in Fig. 3(a) and measured elastic modulus of concrete in Section 3.1.2 were used. Furthermore, the following data are used in the calculation: coefficient of thermal expansion of 12.0 10 6/C for concrete and load cell and 24.0 10 6/C for aluminum plates, length of 9.6 and 24.0 cm for load cell and aluminum plates, respectively, and elastic moduli of 20.6 and 7.18 MPa for load cell and aluminum plates, respectively. In Fig. 5, the difference between calculated and experimental results is due to
Fig. 5. Comparison between experimental and calculated results.
the inaccurate input data, such as properties of load cell and concrete as well as inelastic deformation due to creep of concrete.
4. Conclusions From the results obtained using the developed thermal stress measuring device, the following conclusions can be drawn. 1. This device shows the possibility of measuring thermal stress variations of any position in concrete structures using different thermal expansion coefficient plates even though properties of concrete are uncertain. 2. The application of various degrees of constraint can be achieved by using constraint frame material with different thermal expansion coefficient and crosssectional area than those of concrete. 3. A commercialized chamber, which is able to control temperature and humidity, can be used with this developed device.
Acknowledgments
Table 3 Mechanical properties of concrete
Age (days)
Compressive strength (MPa)
Splitting tensile strength (MPa)
Modulus of elasticity ( 104 MPa)
Surface
Interior
Surface
Interior
Surface
Interior
1 2 3
18.4 23.4 26.0
25.4 33.9 34.3
2.59 2.95 3.25
3.04 3.60 3.69
1.96 2.25 2.55
2.65 2.74 2.94
This research was supported by the National Research Laboratory program of Year 2000 (2000-NNL-01-C-033) from the Ministry of Science and Technology of Korea for the development of cracking Control Technique of Concrete Structure. This support is deeply appreciated. The financial support to the first author by a fund of the National Research Laboratory program of Year 2000 (2000-N-NL-01-C-162) is also gratefully appreciated.
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